arXiv subjects

Kemal Firdaus

Publications and source records attributed to Kemal Firdaus.

3 recordsLinked to original sources

arXiv2026

Two-Dimensional Locally Adaptive Non-Hydrostatic Extension of Shallow Water Equations

We introduce a two-dimensional non-hydrostatic model for shallow water wave dispersion. The model is based on a locally adapted application of a non-hydrostatic correction to the hydrostatic shallow water equations (SWE) in a predictor-corrector scheme. Applying the non-hydrostatic correction uniformly to the entire domain demands a high computational cost, since an elliptic system of equations needs to be solved for the correction terms. We demonstrate that by determining the area where the non-hydrostatic effects are significant, and applying the correction only locally, the computational effort can be reduced by approximately 40\% without sacrificing accuracy in tsunami-like scenarios. As indicators for the non-hydrostatic effect, we use the ratio between total water depth and surface elevation, as well as horizontal velocity norms. Results are shown for several well-known test cases, including wave trains over a semi-circular shoal, static, and moving bottom tsunami-like wave propagation.

physics.flu-dyn↗

arXiv2025

Locally Adaptive Non-Hydrostatic Shallow Water Extension for Moving Bottom-Generated Waves

We propose a locally adaptive non-hydrostatic model and apply it to wave propagation generated by a moving bottom. This model is based on the non-hydrostatic extension of the shallow water equations (SWE) with a quadratic pressure relation, which is suitable for weakly dispersive waves. The approximation is mathematically equivalent to the Green-Naghdi equations. Applied globally, the extension requires solving an elliptic system of equations in the whole domain at each time step. Therefore, we develop an adaptive model that reduces the application area of the extension and by that the computational time. The elliptic problem is only solved in the area where the dispersive effect might play a crucial role. To define the non-hydrostatic area, we investigate several potential criteria based on the hydrostatic SWE solution. We validate and illustrate how our adaptive model works by first applying it to simulate a simple propagating solitary wave, where exact solutions are known. Following that, we demonstrate the accuracy and efficiency of our approach in more complicated cases involving moving bottom-generated waves, where measured laboratory data serve as reference solutions. The adaptive model yields similar accuracy as the global application of the non-hydrostatic extension while reducing the computational time by more than 50%.

math.NA↗

arXiv2024

Non-Hydrostatic Model for Simulating Moving Bottom-Generated Waves: A Shallow Water Extension with Quadratic Vertical Pressure Profile

We formulate a depth-averaged non-hydrostatic model to solve wave equations with generation by a moving bottom. This model is built upon the shallow water equations, which are widely used in tsunami wave modelling. An extension leads to two additional unknowns to be solved: vertical momentum and non-hydrostatic pressure. We show that a linear vertical velocity assumption turns out to give us a quadratic pressure relation, which is equivalent to Boussinesq-type equations. However, this extension involves a time derivative of an unknown parameter, rendering the solution by a projection method ambiguous. In this study, we derive an alternative form of the elliptic system of equations to avoid such ambiguity. The new set of equations satisfies the desired solubility property, while also consistently representing the non-flat moving topography wave generation. Validations are performed using several test cases based on previous experiments and a high-fidelity simulation. First, we show the efficiency of our model in solving a vertical movement, which represents an undersea earthquake-generated tsunami. Following that, we demonstrate the accuracy of the model for landslide-generated waves. Finally, we compare the performance of our novel set of equations with the linear and simplified quadratic pressure profiles.

math.NA↗